Magnetoresistance of a two-dimensional electron gas with spatially periodic lateral modulations: Exact consequences of Boltzmann's equation

TL;DR

This paper uses Boltzmann's equation to analyze how one-dimensional superlattices influence the magnetoresistance and oscillations in a two-dimensional electron gas, considering various types of spatial modulations.

Contribution

It provides an exact theoretical analysis of the effects of electric, magnetic, and mobility superlattices on electron transport in 2D systems, including numerical calculations of magnetoresistance.

Findings

Magnetic and electric superlattices affect only ρ_xx with homogeneous mobility.

Mobility superlattices influence only ρ_yy in the absence of electric and magnetic modulations.

Numerical results show positive magnetoresistance and Weiss oscillations in different magnetic field regimes.

Abstract

On the basis of Boltzmann's equation, and including anisotropic scattering in the collision operator, we investigate the effect of one-dimensional superlattices on two-dimensional electron systems. In addition to superlattices defined by static electric and magnetic fields, we consider mobility superlattices describing a spatially modulated density of scattering centers. We prove that magnetic and electric superlattices in $x$-direction affect only the resistivity component $\rho_{xx}$ if the mobility is homogeneous, whereas a mobility lattice in $x$-direction in the absence of electric and magnetic modulations affects only $\rho_{yy}$. Solving Boltzmann's equation numerically, we calculate the positive magnetoresistance in weak magnetic fields and the Weiss oscillations in stronger fields within a unified approach.